Thame maintained their ten-point lead at the top of the Ryman Division 1table but were made to work for all three points by Bishop's Stortford at Windmill Stadium on Saturday.
Stortford came into the game with an unbeaten away record and got off to a strong start as Vinnie John twice missed chances.
In the opening minute, a Troy Braham cross found him in space at the far post but John could only hit the side netting.
Three minutes later, he latched on to a poor back pass from Chris Fontaine but was denied by a brave save from Ian Moores.
Thame made them pay by taking the lead when Nando Perna split the Stortford rearguard with a tremendous through ball and Chris Potter did the rest, stroking the ball home from the edge of the box.
With driving rain making life difficult for both sides, Stortford almost equalised in the 39th minute when a Martin Sedgwick's header hit the bar and Moores recovered to save John's follow-up shot.
Mark West had a great chance to extend Thame's lead three minutes into the second half but his header from Justin Lee's cross was off target.
In the 59th minute, United made it 2-0. Jefferson Louis powered to the line and found Fontaine, whose cleaver reverse ball was netted by Potter from eight yards.
Stortford's hopes were raised in the 70th minute when substitute Trevor Paul pulled one back, but Thame restored their two-goal cushion in the 76th minute. Perna was again the architect with a surging run to set up West, who coolly drew out Brooks before steering the ball home for his 18th goal of the season.
The visitors were still a threat and reduced the margin with six minutes remaining through Paul, but Thame stood firm in the closing stages.
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